Randomization of crosstalk probing signals

ABSTRACT

In accordance with an embodiment, the vectoring controller is configured to iterate through successive crosstalk acquisition cycles and, within respective ones of the crosstalk acquisition cycles, to configure sequences of crosstalk probing symbols for transmission over the respective communication lines, to receive sequences of error samples as successively measured by respective receivers coupled to the respective communication lines while the sequences of crosstalk probing symbols are being transmitted, and to determine crosstalk estimates between the respective communication lines based on the sequences of error samples. The vectoring controller is further configured to randomize the successive sequences of crosstalk probing symbols used during the successive crosstalk acquisition cycles, and to iteratively configure the vectoring processor based on the successive crosstalk estimates.

TECHNICAL FIELD OF THE INVENTION

The present invention relates to a method and apparatus for configuringa vectoring processor, the vectoring processor being adapted to mitigatecrosstalk between communication lines.

TECHNICAL BACKGROUND OF THE INVENTION

Crosstalk (or inter-channel interference) is a major source of channelimpairment for Multiple Input Multiple Output (MIMO) wired communicationsystems, such as Digital Subscriber Line (DSL) communication systems.

As the demand for higher data rates increases, DSL systems are evolvingtoward higher frequency bands, wherein crosstalk between neighboringtransmission lines (that is to say transmission lines that are in closevicinity over part or whole of their length, such as twisted copperpairs in a cable binder) is more pronounced (the higher frequency, themore coupling).

Different strategies have been developed to mitigate crosstalk and tomaximize effective throughput, reach and line stability. Thesetechniques are gradually evolving from static or dynamic spectralmanagement, techniques to multi-user signal coordination (or vectoring).

One technique for reducing inter-channel interference is joint signalpreceding: the transmit data symbols are jointly passed through aprecoder before being transmitted over the respective communicationchannels. The precoder is such that the concatenation of the precoderand the communication channels results in little or no inter-channelinterference at the receivers.

A further technique for reducing inter-channel interference is jointsignal post-processing: the received data symbols are jointly passedthrough a postcoder before being detected. The postcoder is such thatthe concatenation of the communication channels and the postcoderresults in little or no inter-channel interference at the receivers.

The choice of the vectoring group, that is to say the set ofcommunication lines, the signals of which are jointly processed, israther critical for achieving good crosstalk mitigation performances.Within a vectoring group, each communication line is considered as adisturber line inducing crosstalk into the other communication lines ofthe group, and the same communication line is considered as a victimline receiving crosstalk from the other communication lines of thegroup. Crosstalk from lines that do not belong to the vectoring group istreated as alien noise and is not canceled.

Ideally, the vectoring group should match the whole set of communicationlines that physically and noticeably interact with each other. Yet,local loop unbundling (imposed by national regulation policies) and/orlimited vectoring capabilities may prevent such an exhaustive approach,in which case the vectoring group would include a sub-set only of allthe physically interacting lines, thereby yielding limited vectoringgains.

Signal vectoring is typically performed within an access node, whereinall the data symbols concurrently transmitted over, or received from,all the communication lines of the vectoring group are available. Forinstance, signal vectoring is advantageously performed within a DigitalSubscriber Line Access Multiplexer (DSLAM) deployed at a Central Office(CO) or as a fiber-fed remote unit closer to subscriber premises (streetcabinet, pole cabinet, building cabinet, etc). Signal precoding isparticularly appropriate for downstream communication (toward customerpremises), while signal post-processing is particularly appropriate forupstream communication (from customer premises).

Linear signal precoding and post-processing are advantageouslyimplemented by means of matrix products.

For instance, a linear precoder performs a matrix-product of a vector oftransmit frequency samples with a precoding matrix, the precoding matrixbeing such that the overall channel matrix is diagonalized, meaning theoff-diagonal coefficients of the overall channel, and thus theinter-channel interference, mostly reduce to zero. Practically, and as afirst order approximation, the precoder superimposes anti-phasecrosstalk pre-compensation signals over the victim line along with thedirect signal that destructively interfere at the receiver with theactual crosstalk signals from the respective disturber lines.

Similarly, a linear postcoder performs a matrix-product of a vector ofreceived frequency samples with a crosstalk cancellation matrix, thecrosstalk cancellation matrix being such that the overall channel matrixis diagonalized too.

It is of utmost importance thus to get an accurate estimate of theactual crosstalk channels in order to appropriately initialize or updatethe coefficients of the preceding matrix or of the crosstalkcancellation matrix. In the recommendation entitled “Self-FEXTCancellation (Vectoring) For Use with VDSL2 Transceivers”, ref, G.993.5,and adopted by the International Telecommunication Union (ITU) on April2010, the transceivers are configured to send downstream and upstreampilot sequences over the so-called SYNC symbols, which occurperiodically after every 256 DATA symbols.

On a given victim line, error samples, which comprise both the real andimaginary part of the slicer error (or receive error vector) as measuredfor a specific SYNC symbol on a per tone or group-of-tones basis, arereported to a vectoring controller for further crosstalk estimation. Theerror samples are correlated with a given pilot sequence transmittedover a given disturber line in order to obtain the crosstalk coefficientfrom that disturber line. To reject the crosstalk contribution from theother disturber lines, the pilot sequences are made orthogonal to eachother, for instance by using Walsh-Haclamard sequences comprising ‘+1’and ‘−1’ anti-phase symbols. The crosstalk estimates are used forinitializing or updating the coefficients of the precoding matrix or ofthe crosstalk cancellation matrix.

Once new coefficients are in force in the precoder or postcoder, theresidual crosstalk continue to be tracked, being on account of acrosstalk channel variation, a residual error in the crosstalkestimates, or an approximation in the determination of the precoder orpostcoder coefficients. This is typically achieved by means of iterativeupdate methods that gradually converge towards the optimal precoder orpostcoder coefficients.

In the idealized linear model, orthogonal pilot sequences as per G.993.5recommendation are very effective and always produce accurate andunbiased estimates of the crosstalk channels (initialization) or of theresidual crosstalk channels (tracking). Yet, due to non-linear effects,the crosstalk estimates can have an undesired offset (or bias) thatdrives the precoder or postcoder coefficients away from their optimalvalues.

In high crosstalk environments for instance, the sum of the crosstalkvectors from all the pilot symbols transmitted over all the disturberlines can be such that the received frequency sample goes beyond thedecision boundary of the demodulator. If so, the error vector isreported against the wrong constellation point, yielding an offset inthe estimate of the nominal or residual crosstalk channel.

In G.993.5 recommendation, the transmit vector is estimated by thereceiver. The set of vectors that can be used as pilots is restricted totwo states: a normal state (+1) and an inverted state (−1), which isequivalent to Binary Phase Shift Keying (BPSK) modulation. The receiverdetermines the expected transmit vector by determining in whichhalf-plane the receive vector is, and by selecting the correspondingconstellation point as the most probable transmit vector (minimumdistance criteria). This operation is referred to as demapping.Alternatively, Quadrature Phase Shift Keying (QPSK or 4-QAM)constellation grid can be used for pilot, detection (although only 2constellation points out the possible 4 are effectively used), in whichcase demapping is based on determining the most probable quadrant.

In the event of demapping errors, that is to say when the receiverselects a constellation point different from the transmit, constellationpoint, the reported slicer error has a completely wrong value. Thisleads to major inaccuracies in the calculation of the crosstalkcoefficients, and thus of the precoder and postcoder coefficients, asthe vectoring controller is unaware of the fact that a demapping errorhas occurred within the receiver.

A possible known solution for dealing with demapping errors would be touse multiple demapping decisions across multiple tones. Given that allprobe tones in a particular SYNC symbol are all modulated with the sameparticular bit from of a given pilot sequence, one can use multipletones to do a joint estimation. This technique is more robust than thestraightforward per-tone decision, but in very low Signal to Noise Ratio(SNR) environments, the receiver could still make a wrong decision. IfFrequency Dependent Pilot Sequence (FDPS) is used, the technique canstill be applied, using the fact that the pilot values repeatperiodically after a given number of tones.

Yet, experiments in the field indicate that at least some receivermodels keep on using per-tone decision, with either a BP5K or 4-QAMdemodulation grid, thereby increasing the likelihood of demappingerrors.

Another example of non-linear effects is signal clipping. Still in highcrosstalk environments, the sum of the crosstalk vectors from all thepilot, symbols transmitted over all the disturber lines can be such thatthe receive frequency sample goes beyond the maximum value supported bythe digital processing logic. The error samples would then carry a wrongbounded value that would severely affect and bias the crosstalkestimation process.

Another example of non-linear effects is quantization at various pointsin the signal path. Quantization makes that these signals can only usecertain values. This leads to an offset in the estimate of the residualcrosstalk channel.

Using long-term periodic pilots may thus cause biases to build up andmay lead to performance degradation over time and instability.

SUMMARY OF THE INVENTION

It is an object of the present invention to alleviate or overcome theaforementioned shortcomings and drawbacks of the known solutions.

In accordance with a first aspect of the invention, a vectoringcontroller for controlling a vectoring processor that mitigatescrosstalk between communication lines of a vectoring group is adapted toiterate through successive crosstalk acquisition cycles and, withinrespective ones of the crosstalk acquisition cycles, to configuresequences of crosstalk probing symbols for transmission over therespective communication lines, to receive sequences of error samples assuccessively measured by respective receivers coupled to the respectivecommunication lines while the sequences of crosstalk probing symbols arebeing transmitted, and to determine crosstalk estimates between therespective communication lines based on the sequences of error samples.The vectoring controller is further adapted to randomize the successivesequences of crosstalk probing symbols used during the successivecrosstalk acquisition cycles, and to iteratively configure the vectoringprocessor based on the successive crosstalk estimates.

In one embodiment of the invention, the successive sequences ofcrosstalk probing symbols are randomized by successive arbitraryselection of crosstalk probing sequences within a set of mutuallyorthogonal sequences for modulation of the respective sequences ofcrosstalk probing symbols.

In one embodiment of the invention, the successive sequences ofcrosstalk probing symbols are randomized by successive arbitraryrotation in the frequency domain of some or all of the sequences ofcrosstalk probing symbols.

In one embodiment of the invention, the rotated transmit frequencysamples of the successive sequences of crosstalk probing symbolscoincide with constellation points of a reference constellation gridused for modulation of the crosstalk probing symbols, thereby yielding alimited set of allowed rotation values.

In one embodiment of the invention, the vectoring controller is furtheradapted to evenly distribute the allowed rotation values across therespective communication lines of the vectoring group for rotation ofthe sequences of crosstalk probing symbols.

In one embodiment of the invention, the reference constellation grid isa Binary Phase Shift Keying BPSK constellation grid, and the allowedrotation values are multiples of 180°.

In one embodiment of the invention, the reference constellation grid isa 4-QAM constellation grid, and the allowed rotation values aremultiples of 90°.

In one embodiment of the invention, the amount of applied rotation isarbitrarily selected between 0° and 360°, and the vectoring controlleris further adapted to send successive rotation information to thereceivers indicative of successive rotation values to be applied toreceive frequency samples of the respective sequences of crosstalkprobing symbols.

In one embodiment, of the invention, the successive sequences ofcrosstalk probing symbols are randomized by successive arbitrary scalingof some or all of the sequences of crosstalk probing symbols. Thevectoring controller is further adapted to send successive scalinginformation to the receivers indicative of successive scaling values tobe applied to receive frequency samples of the respective sequences ofcrosstalk probing symbols.

In one embodiment of the invention, the error samples are indicative oferror vectors between received frequency samples of the crosstalkprobing symbols and respective selected constellation points onto whichthe received frequency samples are demapped.

Such a vectoring controller typically forms part, of an access node thatsupports wired communication with subscriber devices over an accessplant, such as a DSLAM, an Ethernet switch, an edge router, etc, anddeployed at a CO or as a fiber-fed remote unit closer to subscriberpremises (street cabinet, pole cabinet, building cabinet, etc).

In accordance with another aspect of the invention, a method forcontrolling a vectoring processor that mitigates crosstalk betweencommunication lines of a vectoring group iterates through successivecrosstalk acquisition cycles respectively comprising configuringsequences of crosstalk probing symbols for transmission over therespective communication lines, receiving sequences of error samples assuccessively measured by respective receivers coupled to the respectivecommunication lines while the sequences of crosstalk probing symbols arebeing transmitted, and determining crosstalk estimates between therespective communication lines based on the sequences of error samples.The method further comprises randomizing the successive sequences ofcrosstalk probing symbols used during the successive crosstalkacquisition cycles, and iteratively configuring the vectoring processorbased on the successive crosstalk estimates.

Embodiments of a method according to the invention correspond with theembodiments of a vectoring controller according to the invention.

Instead of keeping the pilot signals assigned to the vectored linesunchanged for the full duration of showtime, the vectoring controllerintroduces randomness or pseudo-randomness between the successivecrosstalk acquisition cycles that are used for tracking the residualcrosstalk channels. The [pseudo-] randomization is such that a given setof pilots does not re-occur (with high probability, or most of the time)until after many further cycles with different sets of pilots haveoccurred. This intentional [pseudo-]randomness mitigates theaforementioned bias effects so that, after appropriate smoothing,convergence to the optimal precoder or postcoder coefficients isachieved.

One may for instance reshuffle the pilot sequences assigned to thevectored lines for modulation of the pilot symbols between thesuccessive crosstalk acquisition cycles. The re-shuffling can be random,pseudo-random, or may follow some cyclic; or predefined pattern.

Alternatively or in combination with the pilot sequence re-shuffling,one may vary the phase and/or amplitude of the pilot signals. In orderto fulfill the orthogonality requirement, the amount of applied rotationand/or scaling needs to remain constant during the whole length of onecrosstalk acquisition cycle.

If the amount of applied rotation and/or scaling is arbitrarilyselected, then rotation and/or scaling information need to be sent tothe receivers so as the received frequency samples of the pilot, symbolsare appropriately re-equalized.

Yet, one may rotate a pilot signal so as the resulting rotated transmitfrequency samples still coincide with allowed transmit constellationpoints. This embodiment is rather advantageous as the receivers do notneed to be notified about the amounts of applied rotation, and thus iscompatible with the current VDSL2 standard. For instance, if BPSK isused for demodulation of the pilot symbols, then the amount of appliedrotation is selected to be either 0° or 180°. If 4-QAM is used instead,then the amount of applied rotation is selected to be either 0°, 90°,180°, or 270°.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects and features of the invention will becomemore apparent and the invention itself will be best understood byreferring to the following description of an embodiment taken inconjunction with the accompanying drawings wherein:

FIG. 1 represents an overview of an access plant;

FIG. 2 represents an access node as per the present invention;

FIG. 3 is an illustration of the technical effects of the presentinvention in the In-Phase/Quadrature (I/Q) plane; and

FIGS. 4A and 4B are simulation plots for the achieved SNR without andwith pilot randomization respectively.

DETAILED DESCRIPTION OF THE INVENTION

There is seen in FIG. 1 an access plant 1 comprising a network unit 10at a CO, a remotely-deployed access node 20 coupled via one or moreoptical fibers to the network unit 10, and further coupled via a copperloop plant to Customer Premises Equipment (CPE) 30 at various subscriberpremises.

The copper loop plant comprises a common access segment 40, wherein thesubscriber lines are in close vicinity with each other and thus inducecrosstalk into each other, and dedicated loop segments 50 with weakinteractions for final connection to the subscriber premises. Thetransmission media is typically composed of copper Unshielded TwistedPairs (UTP).

The access node 20 comprises a vectoring processor for jointlyprocessing the data symbols that are being transmitted over, or receivedfrom, the loop plant in order to mitigate the crosstalk induced withinthe common access segment 40 and to increase the communication datarates achievable over the respective subscriber lines.

There is seen in FIG. 2 an access node 100 as per the present inventioncoupled to N CPEs 200 ₁ to 200 _(N) through N respective transmissionlines L₁ to L_(N), which are assumed to form part of the same vectoringgroup.

The access node 100 comprises:

-   -   N DSL transceivers 110 ₁ to 110 _(N);    -   a Vectoring Processing Unit 120 (or VPU); and    -   a Vectoring Control Unit 130 (or VCU) for controlling the        operation of the VPU 120.

The transceivers 110 are individually coupled to the VPU 120 and to theVCU 130. The VCU 130 is further coupled to the VPU 120.

The transceivers 110 respectively comprise:

-   -   a Digital Signal Processor (DSP) 111; and    -   an Analog Front End (AFE) 112.

The CPEs 200 comprise respective DSL transceivers 210.

The DSL transceivers 210 respectively comprise:

-   -   a Digital Signal Processor (DSP) 211; and    -   an Analog Front End (AFE) 212.

The AFEs 112 and 212 respectively comprise a Digital-to-Analog Converter(DAC) and an Analog-to-Digital Converter (ADC), a transmit filter and areceive filter for confining the signal energy within the appropriatecommunication frequency bands while rejecting out-of-band interference,a line driver for amplifying the transmit signal and for driving thetransmission line, and a Low Noise Amplifier (LNA) for amplifying thereceive signal with as little noise as possible.

The AFEs 112 and 212 further comprise a hybrid for coupling thetransmitter output to the transmission line and the transmission line tothe receiver input while achieving low transmitter-receiver couplingratio, impedance-matching circuitry for adapting to the characteristicimpedance of the transmission line, and isolation circuitry (typically atransformer).

The DSPs 111 and 211 are respectively configured to operate downstreamand upstream DSL communication channels.

The DSPs 111 and 211 are further configured to operate downstream andupstream DSL control channels that are used to transport DSL controltraffic, such as diagnosis or management commands and responses. Controltraffic is multiplexed with user traffic over the DSL channel.

More specifically, the DSPs 111 and 211 are for encoding and modulatinguser and control data into digital data symbols, and for de-modulatingand decoding user and control data from digital data symbols.

The following transmit steps are typically performed within the DSPs 111and 211:

-   -   data encoding, such as data multiplexing, framing, scrambling,        error control encoding, and data interleaving;    -   signal modulation, comprising the steps of ordering the carriers        according to a carrier ordering table, parsing the encoded bit        stream according to the respective bit loadings of the ordered        carriers, and mapping each chunk of bits onto an appropriate        transmit constellation point (with respective carrier amplitude        and phase), possibly with Trellis coding;    -   signal scaling;    -   Inverse Fast Fourier Transform (IFFT);    -   Cyclic Prefix (CP) insertion; and possibly    -   time-windowing.

The following receive steps are typically performed within the DSPs 111and 211:

-   -   CP removal, and possibly time-windowing;    -   Fast Fourier Transform (FFT);    -   Frequency Equalization (FEQ);    -   signal de-modulation and detection, comprising the steps of        applying to each and every equalized frequency sample an        appropriate constellation grid, the pattern of which depends on        the respective carrier bit loading, detecting the expected        transmit constellation point and the corresponding transmit bit        sequence, possibly with Trellis decoding, and re-ordering all        the detected chunks of bits according to the carrier ordering        table; and    -   data decoding, such as data de-interleaving, error detection        and/or correction, de-scrambling, frame delineation and        de-multiplexing.

The DSPs 111 are further configured to supply transmit frequency samplesto the VPU 120 before Inverse Fast Fourier Transform (IFFT) step forjoint signal precoding, and to supply receive frequency samples to theVPU 120 after Fast Fourier Transform (FFT) step for joint signalpost-processing.

The DSPs 111 are further configured to receive corrected frequencysamples from the VPU 120 for further transmission or detection.Alternatively, the DSPs 111 may receive correction samples to add to theinitial frequency samples before further transmission or detection.

The VPU 120 is configured to mitigate the crosstalk induced over thetransmission lines. This is achieved by multiplying a vector of transmitfrequency samples with a precoding matrix P so as to pre-compensate anestimate of the expected crosstalk (downstream), or by multiplying avector of received frequency samples with a crosstalk cancellationmatrix Q so as to post-compensate an estimate of the incurred crosstalk(upstream).

In the matrix P or Q, a row n represents a particular victim line L_(n),while a column m represents a particular disturber line L_(m). At theintersection, the coupling coefficient that should be applied to thecorresponding disturber transmit or receive frequency sample formitigating over the victim line L_(n) the crosstalk from the disturberline L_(m). Not all the coefficients of the matrix need to bedetermined, for instance on account of limited vectoring capabilitiesfirst assigned to the strongest crosstalkers, or still for instance dueto the fact that some lines do not noticeably interact with each other.The undetermined coefficients are preferably set to 0.

Also, it is noteworthy that a communication line L_(n) for whichvectoring operation is not supported or not enabled, such as a legacyline, yet that still noticeably interferes with other communicationlines, is only considered as a disturber line within the vectoringgroup. The off-diagonal coefficients of the corresponding n^(th) row ofthe matrix P or Q are thus all set to 0.

The VCU 130 is basically for controlling the operation of the VPU 120,and more specifically for estimating the crosstalk coefficients betweenthe transmission lines of the vectoring group, and for initializing andupdating the coefficients of the precoding matrix P and of the crosstalkcancellation matrix Q from the so-estimated crosstalk coefficients.

The VCU 130 is further for controlling the vectoring operation of thetransceivers 110 and 210 by appropriately configuring and adjusting thevectoring parameters.

The VCU 130 starts first by configuring the respective downstream pilotsequences for use by the transceivers 110 for modulation of thedownstream pilot symbols, and the upstream pilot sequences for use bythe transceivers 210 for modulation of the upstream pilot symbols. Thesame pilot sequence is assumed to be used for both upstream anddownstream, although distinct pilot sequences could be configured aswell. The pilot sequences assigned to the transmission lines L₁ to L_(N)are denoted as {S_(nt)}_(n=1 . . . N,t=0 . . . L-1), wherein t denotes apilot symbol index and L denotes the length of the pilot sequences. Afurther distinction is made in FIG. 2 between downstream pilot sequences(k==DS denoting the set of carrier indexes used for downstreamcommunication) versus upstream pilot sequences (k==US denoting the setof carrier indexes used for upstream communication).

The pilot sequences {S_(nt)}_(n=1 . . . N,t=0 . . . L-1) are chosen froma set 131 of mutually orthogonal pilot sequences{W_(mt)}_(m=1 . . . M,t=0 . . . L-1) of size M. In order to fulfill theorthogonality requirement, the size M of the set of mutually orthogonalpilot sequences 131 shall be greater than or equal to the number N ofvectored lines, and less than or equal to the length L of the pilotsequences.

The VCU 130 gathers respective slicer errors{E_(nt)}_(n=1 . . . N,T=0 . . . L-1) as measured during the detection ofthe pilot symbols by the remote transceivers 210 for downstreamcommunication, and by the local transceivers 110 for upstreamcommunication.

The VCU 130 correlates the error samples {E_(nt)}_(t=0 . . . L-1) on arespective victim line L_(n) with the pilot sequence{S_(mt)}_(t=0 . . . L-1) transmitted over a respective disturber lineL_(m) in order to estimate the crosstalk or residual crosstalkcoefficient from the disturber line L_(m) into the victim line L_(n).

The new crosstalk or residual crosstalk estimates are then used forinitializing or updating the coefficients of the precoding matrix P orof the crosstalk cancellation matrix Q.

In order to mitigate the non-linear effects that biases the crosstalkestimation process, such as error quantization, error clipping anddemapping errors, the VCU 130 introduces some [pseudo-]randomnessbetween the successive crosstalk acquisition cycles that are used forrefining the coefficients of the precoding matrix P or of the crosstalkcancellation matrix Q.

In a first embodiment, the VCU 130 re-shuffles the pilot sequencesassigned to the transmission lines L₁ to L_(N) between successivecrosstalk acquisition cycles.

More specifically, before a first crosstalk acquisition round, the VCU130 makes a first [pseudo-]random selection {S_(nt)⁽⁰⁾}_(n=1 . . . N,t=0 . . . L-1) within the set 131 for assignment tothe transmission lines L₁ to L_(N), and configures the transceivers 110and 210 accordingly. The VCU 130 gathers first slicer errors {E_(nt)⁽⁰⁾}_(n=1 . . . N,t=0 . . . L-1) while first pilot symbols modulatedwith the first pilot sequences {S_(nt) ⁽⁰⁾}_(n=1 . . . N,t=0 . . . L-1)are being transmitted over the respective transmission lines L₁ toL_(N), and determines first crosstalk estimates {{circumflex over(θ)}_(nm) ⁽⁰⁾}_(n=1 . . . N;m=1 . . . N) between the respectivetransmission lines (or a subset thereof) by correlating the first errorsamples {E_(nt) ⁽⁰⁾}_(n=1 . . . N,t=0 . . . L-1) with the respectivepilot sequences {S_(mt) ⁽⁰⁾}_(m=1 . . . N,t=0 . . . L-1).

Before a second subsequent crosstalk acquisition cycle takes place, theVCU 130 makes a second [pseudo-]random selection {S_(nt)⁽¹⁾}_(n=1 . . . N,t=0 . . . L-1) within the set 131 for assignment tothe transmission lines L₁ to L_(N), and configures the transceivers 110and 210 accordingly. The VCU 130 gathers second slicer errors{E_(nt)}_(n=1 . . . N,t=0 . . . L-1) while second pilot symbolsmodulated with the second pilot sequences {S_(nt)⁽¹⁾}_(n=1 . . . N,t=0 . . . L-1) are being transmitted over therespective transmission lines L₁ to L_(N), and determines secondcrosstalk estimates {{circumflex over (θ)}_(nm)⁽¹⁾}_(n=1 . . . N;m=1 . . . N) between the respective transmission lines(or a subset thereof) by correlating the first error samples {E_(nt)⁽¹⁾}_(n=1 . . . N,T=0 . . . L-1) with the respective pilot sequences{S_(mt) ⁽¹⁾}_(m=1 . . . N,T=0 . . . L-1).

The process may be repeated again and again with further randomselections {S_(nt)(i)}_(n=1 . . . N,T=0 . . . L-1) to obtain furthercrosstalk estimates {{circumflex over (θ)}_(nm)^((i))}_(n=1 . . . N;m=1 . . . N).

As an alternative to the [pseudo-] random assignment, of the pilotsequences, the VCU 130 could cycle through the set 131 (e.g., firstW₁>L₁ W₂>L₂ . . . W_(N)>L_(N); next W₂>L₁ W₃>L₂ . . . W₁>L_(N); etc), orfollow any pre-defined pattern. Preferably, such a pattern should gothrough a relatively large number of cycles before repeating the sameassignment.

In a second embodiment, which can be used in combination with the pilotre-shuffling, the VCU 130 alters the phase and/or amplitude of the pilotsymbols used during successive crosstalk acquisition cycles.

More specifically, before a first crosstalk acquisition round, the VCU130 makes a first [pseudo-]random selection {S_(nt)⁽⁰⁾}_(n=1 . . . N,T=0 . . . L-1) within the set 131 for assignment tothe transmission lines L₁ to L_(N), and configures the transceivers 110and 210 accordingly. The VCU 130 gathers first, slicer errors {E_(nt)⁽⁰⁾}_(n=1 . . . N,T=0 . . . L-1) while first pilot symbols modulatedwith the first pilot sequences {S_(nt) ⁽⁰⁾}_(n=1 . . . N,T=0 . . . L-1)are being transmitted over the respective transmission lines L₁ toL_(N), and determines first crosstalk estimates {{circumflex over(θ)}_(nm) ⁽⁰⁾}_(n=1 . . . N;m=1 . . . N) between the respectivetransmission lines (or a subset thereof) by correlating the first errorsamples {E_(nt)}_(n=1 . . . N,T=0 . . . L-1) with the respective pilotsequences {S_(mt) ⁽⁰⁾}_(m=1 . . . N,T=0 . . . L-1).

Before a second subsequent crosstalk acquisition cycle takes place, theVCU 130 determines a set of complex factors {n⁽¹⁾}_(n=1 . . . N) toapply to the respective pilot sequences {S_(nt)⁽⁰⁾}_(n=1 . . . N,T=0 . . . L-1) to yield altered pilot sequences{S_(nt) ⁽¹⁾=n⁽¹⁾·S_(nt) ⁽⁰⁾}_(n=1 . . . N,T=0 . . . L-1). If |n⁽¹⁾|=1then we may say that the pilot symbols are rotated by a given amount inthe complex plane. If n⁽¹⁾ is real and |n⁽¹⁾|≠1 then the pilot symbolsare scaled down or up. The complex factors {n⁽¹⁾}_(n=1 . . . N) to applyto the initial pilot sequences {S_(nt) ⁽⁰⁾}_(n=1 . . . N,T=0 . . . L-1),or alternatively the altered pilot sequences {S_(nt)⁽¹⁾}_(n=1 . . . N,T=0 . . . L-1), are communicated to the transmitters110 (downstream) and 210 (upstream) so as they can appropriately alterthe corresponding pilot symbols. The VCU 130 gathers second slicererrors {E_(nt)}_(n=1 . . . N,T=0 . . . L-1) while second pilot symbolsmodulated with the altered pilot sequences {S_(nt)⁽¹⁾}_(n=1 . . . N,T=0 . . . L-1) are being transmitted over therespective transmission lines L₁ to L_(N), and determines secondcrosstalk estimates {{circumflex over (θ)}_(nm)⁽¹⁾}_(n=1 . . . N;m=1 . . . N) between the respective transmission lines(or a subset thereof) by correlating the first error samples {E_(nt)⁽¹⁾}_(n=1 . . . N,T=0 . . . L-1) with the respective pilot sequences{S_(mt) ⁽¹⁾}_(m=1 . . . N,T=0 . . . L-1).

The process may be repeated again and again with further arbitrary setsof complex factors {n^((i))}_(n=1 . . . N) to obtain further crosstalkestimates {{circumflex over (θ)}_(nm) ^((i))}_(n=1 . . . N;m=1 . . . N).

The set of complex factors {n^((i))}_(n=1 . . . N) can be determined[pseudo-]randomly, for example with unit magnitude and phase uniformlydistributed between 0° and 360°. If so, the complex factors n^((i)), oralternatively the altered pilot sequences {S_(n) ^((i))}_(n=1 . . . N),need to be communicated to the respective receivers 210 (downstream) and110 (upstream) so as they can appropriately equalize the so-alteredpilot symbols and measure meaningful slicer errors for furtherreporting.

Alternatively, the complex factors n^((i)) may be chosen from arestricted set of allowed values in order to avoid ad-hoc equalizationof the pilot symbols at the receivers. Indeed, if BPSK is used then thecomplex factors n^((i)) are chosen from the set {1; −1}; if 4-QAM isused then the complex factors n^((i)) are chosen from the set {+1; +j;−1; −j}. If so, the rotated transmit frequency samples still coincidewith valid transmit constellation points, and the complex factors do notneed to be communicated to the receivers for ad-hoc equalization.

Also, the allowed rotation values need to be evenly distributed amongthe transmission lines L₁ to L_(N). For instance, if BPSK is used, it isbeneficial if approximately half of the transmission lines are assignedthe value +1, meaning their pilot signal is left unchanged, while halfof the transmission lines are assigned the value −1, meaning their pilotsignal is rotated by 180°. If 4-QAM is used, it is beneficial ifapproximately a quarter of the transmission lines are assigned the value+1 (0°), a quarter the value j (+90°), a quarter the value −1 (+180°),and a quarter the value −j (+270°).

The successive crosstalk estimates {{circumflex over (θ)}_(nm)^((i))}_(n=1 . . . N;m=1 . . . N) are then used for configuring the VPU120. As the estimation errors caused by non-linear effects in each cycledepend on the pilot sequences used, and as the pilot sequences used insuccessive cycles are randomized, the estimation errors obtained insuccessive cycles are expected to exhibit low correlation or beuncorrelated. After a certain number of iterative updates, the impactsof the aforementioned estimation errors are thus expected to beprogressively annihilated, ultimately yielding unbiased precoder orpostcoder coefficients that achieves near-optimal bit rates over thetransmission lines L₁ to L_(N).

The VCU 130 may use different methods to configure the VPU 120.

For instance, the VCU 130 computes a weighted combination of the first,second and further crosstalk estimates to yield an average crosstalkestimate, which is next used to initialize or to refine the precodingmatrix P or the crosstalk cancellation matrix Q.

Alternatively, the VCU 130 acquires the first crosstalk estimates andinitializes the precoding matrix P or the crosstalk cancellation matrixQ based on these first crosstalk estimates. The VCU 130 may then use thesecond and further crosstalk estimates to successively refine thecoefficients of the precoding matrix P or of the crosstalk cancellationmatrix Q. The first crosstalk estimates is typically obtained during aninitialization phase (init), while the second and further crosstalkestimates are obtained during an active communication phase (show time).

Still alternatively, the VCU 130 may use the first, second and furthercrosstalk estimates to successively refine the coefficients of theprecoding matrix P or of the crosstalk cancellation matrix Q insuccessive steps. The first, second and further crosstalk estimates aretypically obtained during an active communication phase (show time).

The pilot signals do not need to be changed after each and every pilotcycle (a pilot cycle is meant to be the transmission of L consecutivepilot symbols). For instance, on account of the incurred signalingoverload needed for re-configuring the upstream pilot signals, the VCU130 may wait a given number of pilot cycles with a given set of pilotsconfigured before switching to another set of pilots.

Also, not all pilot cycles are used for crosstalk estimation. Forinstance, on account of the incurred processing load, the VCU 130 mayskip a few pilot, cycles without estimating the residual crosstalk.

Also, the VCU 130 may perform more than one crosstalk acquisition cyclesand determine more than one crosstalk estimates while a given set ofpilots is configured, and use all these crosstalk estimates to configurethe VPU 120.

We now give a mathematical model for a DSL system as per FIG. 2, and wederive an algorithm for estimating the crosstalk or residual crosstalkcoefficients, and for appropriately configuring the VPU 120.

Channel Model

Consider a system with N DSL lines L₁ to L_(N) in a vectoring group.Communication takes place on K DMT tones, labeled 0 through K-1. Thetones may be thought as independent channels; we focus attention on aspecific tone k. In general we will use a subscript k to denote the toneindex whenever necessary. Both downstream and upstream operations areconsidered.

In a frequency-domain model of the system, let complex signals x be thevector of complex signals to be sent downstream on lines L₁ to L_(N) (ona particular tone k), where is a diagonal matrix with entries nn=n,where n² is the transmit power on line L_(n), and where x_(n) is a unitpower complex signal to be transmitted downstream onto line L_(n). Then,in the absence of vectoring, the received signal is given by:

{tilde over (r)}=H

x+{tilde over (z)},

wherein H is a N×N channel matrix, with element H_(nn) representingdirect channel gain and element H_(nm) representing crosstalk channelgain from line L_(m) into line L_(n),and wherein {tilde over (z)} represents background noise.

If we apply precoding with precoding matrix P=l+C, we have:

{tilde over (r)}={tilde over (R)}

x+{tilde over (z)},

wherein {tilde over (R)}=H(I+C) is the residual channel matrix.

We decompose the channel matrix as:

H=D(I+G),

wherein D is a diagonal matrix of direct gains D_(nn)=H_(nn),and wherein G is the receiver-referred relative crosstalk channel matrixwith entries G_(nm)=H_(nm)/H_(nn) for m≠n and G_(nn)=0.

Prior to slicing the received signal on a fixed grid, the receivedsignal passes through a Frequency domain Equalizer (FEQ), and thetransmit power is compensated for. The result of these two operations isthe normalized received signal:

r=Λ ⁻¹ D ⁻¹ {tilde over (r)}=Λ ⁻¹ RΛx+z=x+Λ ⁻¹ θΛx+z,

wherein R=D⁻¹{tilde over (R)}=(I+G)(I+C) and z=Λ⁻¹D⁻¹{tilde over (z)}are the normalized residual channel matrix and background noiserespectively, and wherein =R−I=G+C+GC is the normalized residualcrosstalk channel matrix.

During SYNC symbols, the transmitted values x_(n) can be estimated withhigh reliability by the receiver, and subtracted from the receivedsignal to form an error signal. In vector form the error signal is givenby:

e=r−x=Λ ⁻¹ θΛx+z  (1).

When error feedback is operational, these complex error values are sentback to the vectoring controller, and can be used to estimate thenormalized residual crosstalk channel matrix, which we wish to drive tozero.

Now let complex signals x be the vector of complex signals to be sentupstream on lines L₁ to L_(N) (on a particular tone k), where is adiagonal matrix with entries nn=n, where n² is the transmit power online L_(n), and where x_(n) is a unit power complex signal to betransmitted upstream onto line L_(n). Then, in the absence of vectoring,the received signal is given by:

{tilde over (r)}HΛx+{tilde over (z)},

wherein H is a N×N channel matrix, with element H_(nn) representingdirect channel gain and element H_(nm) representing crosstalk channelgain from line L_(m) into line L_(n), and wherein {tilde over (z)}represents background noise.

In the upstream direction, we decompose the channel matrix as:

H=(I+{tilde over (G)})D,

wherein D is a diagonal matrix of direct gains D_(nn)=H_(nn), andwherein {tilde over (G)} is the transmitter-referred relative crosstalkmatrix with entries {tilde over (G)}_(nm)-H_(nm)/H_(mm) for m≠n and{tilde over (G)}_(nn)=0.

The use of different notations downstream and upstream are useful. Oneimportant property is that with these notations, the relative crosstalkcoefficients are typically much smaller than unity, even when lines ofdifferent lengths are present. In downstream, the channels H_(nm) andH_(nn) both have the same propagation distance; the distance is afunction of the receiver. In upstream on the other hand, it is thechannels H_(nm) and H_(mm) that cover the same propagation distance;here the distance is a function of the transmitter.

We apply postcoding with postcoding matrix Q=I+C, followed by frequencyequalization (FEQ), represented by a diagonal matrix F, and powernormalization. The receiver adapts F to be the inverse of the diagonalof the postcoded channel (I+C)H, which in case of small crosstalk,yields F≈D⁻¹. The compensated signal after these three operations isthus given by:

y=

⁻¹ F(I+C){tilde over (r)}=Λ ⁻¹ FRDΛx+z,

wherein R=(L+C)(L+{tilde over (G)}) is the normalized residual channelmatrix, and wherein the noise term is z=Λ⁻¹F(I+C){tilde over(z)}≈Λ⁻¹D⁻¹{tilde over (z)}.

The noise term depends on the postcoder setting, but this dependence canbe ignored if the coefficients of C are small relative to unity, asshould be the case in practice.

In general, we define =R−I to be the normalized residual crosstalkchannel matrix. We wish to drive this residual crosstalk to zero.

During SYNC symbols, the transmitted values X_(n) can be estimated withhigh reliability by the receiver, and subtracted from the compensatedsignal r to form an error signal. In vector form the error signal isgiven by:

e=y−x=Λ ⁻¹ FθDΛx+z  (2).

When error feedback is operational, these complex error values areforwarded to the vectoring controller, and can be used to estimate theresidual crosstalk channel.

Crosstalk Estimation Algorithm

Because the mapping from the residual crosstalk channel to the errorsamples e is very similar in downstream (1) and upstream (2), theremainder of this description is largely common for upstream anddownstream. However, it should be kept in mind that the quantity z has aslightly different meanings in upstream versus downstream. Also, wherereceiver referred relative crosstalk G is referenced when describingdownstream communication, it should be replaced by thetransmitter-referred relative crosstalk {tilde over (G)} when describingupstream communication.

For pilot-based crosstalk estimation, we send pilot sequences on thepilot symbols. That is, define a N×L pilot matrix S, where S_(nt) is abinary value ‘+1’ or ‘−1’, that will modulate the complex symbol sent,on line L_(n) at time t. The sequence is repeated with period L, that isthe value sent at time t is S_(n) with =t mod L. We choose S to beorthogonal, meaning that SS^(T)==LI_(N), that is L times the N×Nidentity matrix.

Denote by a=(1+j)/√2 the 4-QAM constellation point 00, scaled to unitpower, with −a the point 11. The values sent on the SYNC symbol period tare then x_(n)(t)=aS_(nt).

The L pilot symbols of a given pilot sequence may also be rotated and/orscaled by multiplication with a complex factor _(n), in which case thetransmitted value is X_(n)(t)=a _(n)S_(nt).

For downstream, the error symbols received on all lines over Lconsecutive SYNC symbols can be written in N×L matrix notation as:

E=aA ⁻¹

⁻¹ θ

AS+Z,

wherein A is a diagonal matrix with entries A_(nn)=_(n),wherein A⁻¹ is the ad-hoc equalization for the received pilot symbolsperformed at the receiver.

If n=+/−1, then the equalization factor A⁻¹ is no longer required andcan be omitted. In that case, the receivers estimate AS directly withoutusing knowledge of A, and the error symbols are:

E=a

⁻¹ θ

AS+Z

Correlating the sequence of error samples received on each line witheach of the pilot sequences can be represented in matrix notation byright-multiplying the error matrix E by the transpose of the pilot,sequence. In case of ad-hoc equalization, the resulting unnormalizedcorrelations are of the form:

U=ES ^(T) =aA ⁻¹

⁻¹ θ

ASS ^(T) +ZS ^(T) =aLA ⁻¹

⁻¹ θ

A+ZS ^(T).

Note that this correlation operation only involves adding andsubtracting complex error samples—there are no multiplications required.Finally, the unnormalized correlations are normalized to obtain unbiasedestimates of the residual crosstalk:

$\begin{matrix}{{{\hat{\Theta}}_{nm} = {{{U_{nm}\left( \frac{a_{n}}{a_{m}} \right)}\left( \frac{\sigma_{n}}{\sigma_{m}} \right)\left( \frac{1}{aL} \right)} = {\Theta_{nm} + w_{nm}}}},} & (3)\end{matrix}$

wherein the noise term is:

$W_{nm} = {\begin{pmatrix}v_{n} \\a_{m}\end{pmatrix}\begin{pmatrix}v_{n} \\\sigma_{m}\end{pmatrix}\left( \frac{1}{aL} \right){\sum\limits_{t = 0}^{L - 1}{z_{nt}{s_{mt}.}}}}$

A quick calculation shows that the variance of the crosstalk estimateis:

${{var}\left\lbrack {\hat{\Theta}}_{m} \right\rbrack} = {{E\left\lbrack {W_{nm}}^{2} \right\rbrack} = {\left( \frac{{a_{n}}^{2}}{{a_{m}}^{2}} \right)\left( \frac{\sigma_{n}^{2}}{\sigma_{m}^{2}} \right){\frac{E\left( {Z_{n}}^{2} \right)}{L}.}}}$

For upstream now, the error symbols received on lines L₁ to L_(n) over Lconsecutive SYNC symbols can be written in N×L matrix notation as:

E=aA ⁻¹

⁻¹ FθD

AS+Z,

assuming that the receiver knows and performs ad-hoc equalization of A.

Otherwise, if the receivers directly estimate AS without using knowledgeof A, the error feedback is:

E=a

⁻¹ FθD

AS+Z.

Correlating the sequence of error samples received on each line witheach of the pilot sequences can be represented in matrix notation byright-multiplying the error matrix E by the transpose of the pilotsequence. In case of ad-hoc equalization, the resulting unnormalizedcorrelations are of the form:

U=ES ^(T) =aA ⁻¹

⁻¹ FθD

ASS ^(T) +ZS ^(T) =aLA ⁻¹

⁻¹ FθD

A+ZS ^(T).

Finally, the unnormalized correlations are normalized to obtain unbiasedestimates of the residual crosstalk:

$\begin{matrix}{{{\hat{\Theta}}_{nm} = {{{U_{nm}\left( \frac{a_{n}}{a_{m}} \right)}\left( \frac{\sigma_{n}}{F_{nn}H_{mm}\sigma_{m}} \right)\left( \frac{1}{aL} \right)} = {\Theta_{nm} + w_{nm}}}},} & (4)\end{matrix}$

wherein the noise term is:

$W_{nm} = {\left( \frac{a_{n}}{a_{m}} \right)\left( \frac{v\; \sigma_{n}}{F_{nn}H_{mm}\sigma_{m}} \right)\left( \frac{1}{aL} \right){\sum\limits_{t = 0}^{L - 1}{z_{nt}{s_{mt}.}}}}$

A quick calculation shows that the variance of the crosstalk estimateis:

${{var}\left\lbrack {\hat{\Theta}}_{nm} \right\rbrack} = {{E\left\lbrack {W_{nm}}^{2} \right\rbrack} = {\left( \frac{{a_{n}}^{2}}{{a_{m}}^{2}} \right)\left( \frac{\sigma_{n}^{2}}{{F_{nn}}^{2}{H_{mm}}^{2}\sigma_{m}^{2}} \right){\frac{E\left\lbrack {Z_{n}}^{2} \right\rbrack}{L}.}}}$

Precoder and Postcoder Configuration

The residual crosstalk estimates {{circumflex over (θ)}_(nm)^((i))}_(n=1 . . . N;m=1 . . . N), which are obtained as per equation(3) or (4) during successive crosstalk acquisition cycles, are next usedto iteratively update the precoding matrix P or the crosstalkcancellation matrix Q.

Let P^((i)) denote the precoding matrix during the i^(th) crosstalkacquisition cycle.

Ideally, the new precoding matrix P^((i+1)) shall be determined from theestimate {circumflex over (θ)}^((i)) of the normalized residualcrosstalk channel matrix using the following matrix inversion formula:

P ^((i+1)) =I+C ^((i+1)) =P ^((i)) R ^((i)−1) =P ^((i))(I+θ ^((i)))⁻¹.

Indeed, the new normalized channel matrix will become:

(I+G)P ^((i+1))=(I+G)P ^((i)) R ^((i)−1)=(I+G)(I+C ^((i)))(I+C^((i)))⁻¹(I+G)⁻¹ =I.

Although ideal precoder coefficients are obtained after one iteration,this involves inverting lot of large matrices.

As a first-order approximation, one may subtract the estimated residualcrosstalk from the precoder coefficients as follows:

P ^((i+1)) =I+C ^((i+1)) =P ^((i))−{circumflex over (θ)}^((i)),

thereby yielding:

$\begin{matrix}{{\left( {I + G} \right)P^{({i + 1})}} = {\left( {I + G} \right)\left( {P^{(i)} - {\hat{\Theta}}^{(i)}} \right)}} \\{= {\left( {I + G} \right)\left( {I + C^{(i)} - {\hat{\Theta}}^{(i)}} \right)}} \\{= {I + \Theta^{(i)} - {\hat{\Theta}}^{(i)} - {G\; {\hat{\Theta}}^{(i)}}}} \\{\simeq {I - {G\; {\hat{\Theta}}^{(i)}}}}\end{matrix}$

As the normalized crosstalk coefficients are expected to be low comparedto unity, the residual crosstalk θ^((i+1))=θ^((i))−{circumflex over(θ)}^((i))−G{circumflex over (θ)}^((i))≈−G{circumflex over (θ)}^((i))gets smaller and smaller after each iteration, and the overall channelmatrix is expected to converge towards the identity matrix I.

Alternatively, one may use a multiplicative update as per US patent,application entitled “Multiplicative Updating of Precoder or PostcoderMatrices for Crosstalk Control in a Communication System”, and publishedon Aug. 2, 2012 with publication number US 2012/0195183.

The idea is to use an auxiliary matrix that is an approximation of theinverse of the resultant channel matrix R^((i)), and that is formed bysubtracting the estimate {circumflex over (θ)}^((i)) of the normalizedresidual crosstalk channel matrix from the identity matrix I. Thismultiplicative update process therefore makes the approximation R^((i))⁻¹ ≈I−^((i)) and then multiplies the current precoder matrix P^((i)) onthe right by I−^((i)). The updated precoder matrix P^((i+1)) is thengiven by:

P ^((i+1)) ×I+C ^((i+1)) =P ^((i))(I−{circumflex over (θ)} ^((i))),

and so the updated overall normalized channel matrix is given by:

$\begin{matrix}{{\left( {I + G} \right)P^{({i + 1})}} = {\left( {I + G} \right){P^{(i)}\left( {I - {\hat{\Theta}}^{(i)}} \right)}}} \\{= {\left( {I + G} \right)\left( {I + C^{(i)}} \right)\left( {I - {\hat{\Theta}}^{(i)}} \right)}} \\{= {I + \; {\hat{\Theta}}^{(i)} - {\hat{\Theta}}^{(i)} - {\hat{\Theta}}^{{(i)}2}}} \\{\simeq {I - {\hat{\Theta}}^{{(i)}2}}}\end{matrix}$

The entries of the normalized residual channel matrix are normally muchsmaller than the entries of the normalized crosstalk channel matrix G,and so the error term—² is expected to be much smaller than the errorterm of a typical additive update—G.

One may also introduce respective weights in the iterative updatealgorithm so as to smooth the convergence process and avoid anytransient impairment in case the newly estimated residual crosstalkcoefficients are severely biased (e.g., on account of demapping errors).

Alternative update methods could be used as well, such as the Least MeanSquare (LMS) adaptive algorithm or alike.

A similar derivation is obtained for updating the crosstalk cancellationmatrix Q.

There is seen in FIG. 3 further details as per how randomization of thepilot sequences mitigates the non-linear effects that bias the crosstalkestimation process.

It is assumed that line L₁ is the victim line, and that lines L₂ and L₃are dominant disturbers for the line L₁.

The pilot sequences are assumed to be of length 4. The constant,sequence [+1, +1, +1, +1] is not used as it yields poor estimates in thepresence of constant biases. The three remaining orthogonal sequencesare [+1, −1, +1, −1], [−1, −1, +1, +1] and [+1, −1, −1, +1]. Let usassume that the lines L₁, L₂ and L₃ are initially assigned the pilotsequences S₁ ⁽⁰⁾=[+1, −1, +1, −1], S₂ ⁽⁰⁾=[−1, −1, +1, +1] and S₃⁽⁰⁾=[+1, −1, −1, +1]during a first crosstalk acquisition cycle.

The top I/Q plot shows the normalized residual crosstalk coefficients_(12k) and _(13k) from lines L₂ and L₃ respectively into line L₁ for agiven tone k and during a given crosstalk acquisition cycle. Thisresidual crosstalk is due to several factors, including estimate errorsin equations (3) and (4), non-ideal matrix inversion for thedetermination of the precoding matrix P or the crosstalk cancellationmatrix Q, the inherent inaccuracy of the digital arithmetic, as well asany of the aforementioned non-linear effects that may bias the crosstalkestimates.

The bottom I/Q plot shows the frequency samples of a sequence of pilotsymbols as received over line L₁ at frequency index k during the samecrosstalk acquisition cycle (after channel equalization and powernormalization). Assuming there is no other noise source, the receivedfrequency samples go through positions A1, C2, D1 and B2 depending onwhether +1 or −1 have been transmitted over the respective lines L₁, L₂and L₃. As one can see, some specific combination, presently −1 on lineL₁, −1 on line L₂ and −1 on line L₃, yields signal clipping (position C2is beyond the I/Q signal boundaries). Also, as the received samplesrepeatedly go through a few positions only (4 out of the 8 possiblepositions), there can be some artifacts arising from the quantization ofthese particular points.

In order to mitigate these effects, one could randomize the pilotsignals during a subsequent crosstalk acquisition cycle.

For instance, one could apply 180° rotation to one or more pilotsequences (inc. the victim line), and keep the other pilots unchanged(0°). Presently, during another crosstalk acquisition cycle, the pilotsequences of lines L₃ is inverted, while the pilot sequences of line L₁and L₂ are left unchanged, thereby yielding the following pilotassignment S₁ ⁽¹⁾=[+1, −1, +1, −1], S₂ ⁽¹⁾=[−1, −1, +1, +1] and S₃⁽¹⁾=[−1, +1, +1, −1]. The received frequency samples now go throughdifferent positions, presently positions C1, A2, B1 and D2, therebymitigating the quantization artifacts.

In order to mitigate the signal clipping that occurs when position C2 ishit, one may apply an ad-hoc rotation ² to the pilot sequence of lineL₂, thereby yielding S₂ ⁽²⁾=[−e^(j 2), −e^(j 2), +e^(j 2), +e^(j 2)],and a rotation ₃ to the pilot sequence of line L₃, thereby yielding S₃⁽²⁾=[+e^(j 3), −e^(j 3), −e^(j 3)], while the pilot sequence of line L₁is left unchanged, i.e. S₁ ⁽²⁾=[+1, −1, +1, −1]. The rotated crosstalksignals have been plotted as gray vectors, and as one can see, thesignal clipping is suppressed or at least mitigated.

The present invention is a simple mechanism that avoids constant offsetswhile being (partly) compatible with the current VDSL2 standard. Thepresent invention helps to obtain good stable vectored performance inthe presence of high crosstalk which would otherwise be impaired bydemapping errors, clipping errors, or other non-linear artifacts. Theneed for complex processing to identify and correct demapping errors isavoided, or at least reduced.

There is seen in FIG. 4A a first, simulation plot, wherein the achievedSNR has been plotted on each of 20 active lines at the end of eachtracking cycle, and wherein the same pilot assignment is used across allcrosstalk acquisition cycles. In a tracking cycle, the residualcrosstalk is estimated, and the precoder is updated accordingly. As onecan see, communication lines are gradually affected by degradation,driven by demapping errors in the CPE and other artifacts that causebias in the residual crosstalk estimates and drive the precodercoefficients away from their optimal values.

There is seen in FIG. 4B a second simulation plot, wherein the achievedSNR has been plotted on each of 20 active lines at the end of eachtracking cycle, and wherein the pilots are now randomly re-shuffledbetween successive crosstalk acquisition cycles. As one can see, alllines are stable now. Although demapping errors occur initially, thebias introduced is different in each tracking cycle, and so the systemconverges to the correct solution.

It is to be noticed that the term ‘comprising’ should not be interpretedas being restricted to the components listed thereafter. Thus, the scopeof the expression ‘a device comprising components A and B’ should not belimited to devices consisting only of components A and B. It means thatwith respect to the present invention, the relevant components of thedevice are A and B.

It, is to be further noticed that the term ‘coupled’ should not beinterpreted as being restricted to direct connections only. Thus, thescope of the expression ‘a device A coupled to a device 6’ should not belimited to devices or systems wherein an output of device A is directlyconnected to an input of device B, and/or vice-versa. It means thatthere exists a path between an output of A and an input of B, and/orvice-versa, which may be a path including other devices or means.

The description and drawings merely illustrate the principles of theinvention. It will thus be appreciated that those skilled in the artwill be able to devise various arrangements that, although notexplicitly described or shown herein, embody the principles of theinvention. Furthermore, all examples recited herein are principallyintended expressly to be only for pedagogical purposes to aid the readerin understanding the principles of the invention and the conceptscontributed by the inventor(s) to furthering the art, and are to beconstrued as being without limitation to such specifically recitedexamples and conditions. Moreover, all statements herein recitingprinciples, aspects, and embodiments of the invention, as well asspecific examples thereof, are intended to encompass equivalentsthereof.

The functions of the various elements shown in the figures may beprovided through the use of dedicated hardware as well as hardwarecapable of executing software in association with appropriate software.When provided by a processor, the functions may be provided by a singlededicated processor, by a single shared processor, or by a plurality ofindividual processors, some of which may be shared. Moreover, aprocessor should not be construed to refer exclusively to hardwarecapable of executing software, and may implicitly include, withoutlimitation, digital signal processor (DSP) hardware, network processor,application specific integrated circuit (ASIC), field programmable gatearray (FPGA), etc, Other hardware, conventional and/or custom, such asread only memory (ROM), random access memory (RAM), and non volatilestorage, may also be included.

1. A vectoring controller for controlling a vectoring processor thatmitigates crosstalk between communication lines of a vectoring group,and adapted to iterate through successive crosstalk acquisition cyclesand, within respective ones of the crosstalk acquisition cycles, toconfigure sequences of crosstalk probing symbols for transmission overthe respective communication lines, to receive sequences of errorsamples as successively measured by respective receivers coupled to therespective communication lines while the sequences of crosstalk probingsymbols are being transmitted, and to determine crosstalk estimatesbetween the respective communication lines based on the sequences oferror samples, wherein the vectoring controller is further adapted torandomize the successive sequences of crosstalk probing symbols usedduring the successive crosstalk acquisition cycles, and to iterativelyconfigure the vectoring processor based on the successive crosstalkestimates.
 2. A vectoring controller according to claim 1, wherein thesuccessive sequences of crosstalk probing symbols are randomized bysuccessive arbitrary selection of crosstalk probing sequences within aset of mutually orthogonal sequences for modulation of the respectivesequences of crosstalk probing symbols.
 3. A vectoring controlleraccording to claim 1, wherein the successive sequences of crosstalkprobing symbols are randomized by successive arbitrary rotation in thefrequency domain of some or all of the sequences of crosstalk probingsymbols.
 4. A vectoring controller according to claim 3, wherein therotated transmit frequency samples of the successive sequences ofcrosstalk probing symbols coincide with constellation points of areference constellation grid used for modulation of the crosstalkprobing symbols, thereby yielding a limited set of allowed rotationvalues.
 5. A vectoring controller according to claim 4, wherein thevectoring controller is further adapted to evenly distribute the allowedrotation values across the respective communication lines of thevectoring group for rotation of the sequences of crosstalk probingsymbols.
 6. A vectoring controller according to claim 4, wherein thereference constellation grid is a Binary Phase Shift Keying BPSKconstellation grid, and wherein the allowed rotation values aremultiples of 180°.
 7. A vectoring controller according to claim 4,wherein the reference constellation grid is a 4-QAM constellation grid,and wherein the allowed rotation values are multiples of 90°.
 8. Avectoring controller according to claim 3, wherein the amount of appliedrotation is arbitrarily selected between 0° and 360°, and wherein thevectoring controller is further adapted to send successive rotationinformation to the receivers indicative of successive rotation values tobe applied to receive frequency samples of the respective sequences ofcrosstalk probing symbols.
 9. A vectoring controller according to claim1, wherein the successive sequences of crosstalk probing symbols arerandomized by successive arbitrary scaling of some or all of thesequences of crosstalk probing symbols, and wherein the vectoringcontroller is further adapted to send successive scaling information tothe receivers indicative of successive scaling values to be applied toreceive frequency samples of the respective sequences of crosstalkprobing symbols.
 10. A vectoring controller according to claim 1,wherein the error samples are indicative of error vectors betweenreceived frequency samples of the crosstalk probing symbols andrespective selected constellation points onto which the receivedfrequency samples are demapped.
 11. An access node for providingbroadband communication services to subscribers, and comprising avectoring controller according to claim
 1. 12. An access node accordingto claim 11, wherein the access node is a Digital Subscriber Line AccessMultiplexer DSLAM.
 13. A method for controlling a vectoring processorthat mitigates crosstalk between communication lines of a vectoringgroup, and iterating through successive crosstalk acquisition cyclesrespectively comprising configuring sequences of crosstalk probingsymbols for transmission over the respective communication lines,receiving sequences of error samples as successively measured byrespective receivers coupled to the respective communication lines whilethe sequences of crosstalk probing symbols are being transmitted, anddetermining crosstalk estimates between the respective communicationlines based on the sequences of error samples, wherein the methodfurther comprises randomizing the successive sequences of crosstalkprobing symbols used during the successive crosstalk acquisition cycles,and iteratively configuring the vectoring processor based on thesuccessive crosstalk estimates.